A Fulbright Scholar, Professor Bebbington studied at the University of Melbourne and in New York at Queens College, Columbia University, and the City University of New York Graduate School, completing Masters degrees in Arts, Music, and Philosophy, and a PhD.
Prior to his role at the University of Adelaide, he was Deputy Vice-Chancellor (University Affairs), and previously, Pro Vice-Chancellor (Global Relations) at the University of Melbourne. He also served as a Dean at the University of Melbourne and at the University of Queensland, and before that taught at the Australian National University's School of Music.
As a teacher, he won the University of Melbourne Award for Excellence in Teaching (Humanities) in 2005 and an Australian Learning and Teaching Council Citation for "30 years of outstanding teaching" in 2008. He appears frequently as a visiting keynote speaker at universities in Australia and abroad, including recent addresses in China and Singapore.
Professor Bebbington's publications include the Oxford Companion to Australian Music, and he was, for a decade, the music member of the international Advisory Committee for Encyclopaedia Britannica. His national community roles have included seven years as Chair of Music Committees for the Australia Council and Deputy Chair of Youth Music Australia. He was for many years involved in the management of the Australian Music Examinations Board in Queensland and then Victoria, and in March 2013 received the Fellowship in Music, Australia (FMusA), the highest qualification offered by the AMEB, in recognition of his service.